Empty Set

Q.

A set is a well-defined collection of objects.

1. a collection of similar objects

2. a collection of different objects

Q.

Let $A=\left\{1,2,3,4,5\right\};B=\left\{2,3,6,7\right\}$. Then the number of elements in $(A\times B)\cap (B\times A)$ is

1. $18$

2. $6$

3. $4$

4. $0$

Q. A set having no element is called the ___ set.

Q. The number of distinct elements in a given set A is called the ___ of A.

Q.

The set of even prime numbers that are greater than 2 is a/an _____________.

1. singleton set

2. empty set

3. infinite set

4. disjoint set

Q.

Define equal sets and equivalent sets.

Q.

Define void set.

Q. Which of the following is a subset of every set ?

1. Universal Set
2. {0}
3. Null Set
4. None of the above

Q.

Find the product of first natural number, first whole number and first prime number.

Q.

Which of the following represents the empty set?

1. $\left\{0\right\}$

2. $\left\{\right\}$

3. $\varnothing$

4. $\left\{\varnothing \right\}$

Q. A set having no element is called an empty set.

1. True
2. False

Q. A , B are any non empty sets and n(A) = n(B) can A , B are equal sets ?Justify?

Q. Is zero is a negative number or a positive number ?
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Q.

Which of the following is/are null sets?

1. A = { $x:x\in$ N, 2 < $x$ < 10 }

2. B = { $x:x$ is an even prime number greater than 2 }

3. C = { $x:x$ is a rational number, $x^2$ - 3 = 0 }

4. D = {$x:x$ is an odd natural number divisible by 2}

Q.

Find the product of first natural number and first prime number.

Q.

What is the formula of GP?

Q. ntIf f(x) be a periodic function of period t show that, [ integral f(x) dx, with lower limit a and upper limit a+t] is independent of a.n

Q. A set A contains 3 elements and set B contains 4 elements. The minimum number of elements in $A\cap B$ is

1. 3
2. 4
3. \N
4. 7

Q. If set $A$ = { x : x is an odd natural number} and
set $B$ = { y: y is an even natural number}, then _____________________

1. $A\cup B$ is a finite set.
2. $A\cup B$ is a null set.
3. $A\cap B$ is a null set.
4. $A\cap B$ is an infinite set.

Q.

If A = {Prime numbers between 19 and 23}, then A is __________.

1. an equal set

2. not a set

3. a null set

4. an infinite set

Q.

$A_1,A_2,...,A_{30}$are $30$sets, each having $5$elements and $B_1,B_2,...,B_n$are n sets each with $3$elements. If $\underset{i=1}{\overset{30}{\cup }}{A}_i=\underset{j=1}{\overset{n}{\cup }}{B}_j=S$ and each element of $S$ belongs to exactly $10$ of the $A_i$s and exactly $9$ of the $B_j$s, then the value of $n$ is

1. $15$

2. $3$

3. $45$

4. None of these

Q.

The number of elements in each of universal set, set A and set B are represented as n(U), n(A), n(B) respectively. The number of elements that are not in set A and not in set B is given by

1. n(A ∩ B)^I

2. n(A^I U B^I)

3. n(U) - n(A ∩ B)

4. n(U) - n(A U B)

Q.

Null set should written in list form nd set builder form

Q.

State if True or False.The number of elements in each of universal set , set A and set B are represented as n(U), n(A), n(B) respectively. The number of elements that are not in set A and not in set B is given by n(U) - n(A U B)

1. n(A^I U B^I)

2. n(A ∩ B)^I

Q.

Number of elements in each of the universal set, set A and set B are represented as n(U), n(A), n(B) respectively. The number of elements that are not in set A and not in set B is given by

1. n(A ∩ B)^I

2. n(A^I U B^I)

3. n(U) - n(A U B)

4. n(U) - n(A ∩ B)

Q.

Which of the following sets are finite and which are infinite ?

(i) Set of concentric circles in a plane.

(ii) Set of letter of the English Alphabets.

(iii) {$xϵN;x>5$}

Q. the number of surjections that can be defined from A={1, 2, 8, 9} to b={3, 4, 5, 10} is?

Q.

Let $A=\left\{1,2,3,4\right\}$ $,$ $B=\left\{a,b,c,d\right\}$ and $C=\left\{x:x<5,x\in N\right\}$. State which of the following is true and which is false$.$

$B\leftrightarrow C$

1. True
2. False

Q. $\text{If}f\left(x\right)=x^2-1,\text{and}g\left(x\right)=x-2,$ $\text{then find a, if}gof\left(a\right)=1.$ [2 marks]

Q. Prove that , null set is a subset of all set .